Question

select the correct answer.
a science club has 16 members. how many ways can a president, a vice president, and a treasurer be selected from the members?
a. 96
b. 560
c. 1,120
d. 3,360

Explanation:

Step1: Identify permutation need

We are choosing distinct positions (president, vice president, treasurer), so order matters. We use permutations: $P(n,k)=\frac{n!}{(n-k)!}$ where $n=16$ (total members), $k=3$ (positions).

Step2: Calculate permutation value

$$\begin{align*} P(16,3)&=\frac{16!}{(16-3)!}\\ &=16\times15\times14 \end{align*}$$

Step3: Compute final product

$16\times15=240$, then $240\times14=3360$

Answer:

D. 3,360